Horizon structure of initial-data sets for axisymmetric two-black-hole collisions

The physical content and causal structure of data sets representing two equal-sized black holes with linear or angular momenta are explored by searching for all marginally outer-trapped surfaces. The trapped-surface (or apparent-horizon) equation is posed as a boundary-value problem that, with small changes, will be applicable to nonaxisymmetric systems. In addition to the trapped surfaces surrounding each individual black hole, if the black holes are close enough together or there are appropriate momenta on the holes, then there exist both inner and outer marginally outer-trapped surfaces which bound a trapped region surrounding both holes. With this accurate information on the causal structure of the initial-data sets we can estimate the radiative potential of each data set. In order to help gauge how well the initial-data sets represent the desired physical scenario, we explore two algorithms for estimating the amount of energy in the initially radiative part of the gravitational field.